Problem: Simplify the following expression: $r = \dfrac{2a + 10}{4} \div \dfrac{9a}{10}$
Explanation: Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{2a + 10}{4} \times \dfrac{10}{9a}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ (2a + 10) \times 10 } { 4 \times 9a}$ $r = \dfrac{20a + 100}{36a}$ Simplify: $r = \dfrac{5a + 25}{9a}$